J. Am. Chem. SOC.1990,112,4132-4141
4132
An Investigation of the Relationship between Sweetness and Intramolecular Hydrogen-Bonding Networks in Hexuloses Using the Semiempirical Molecular Orbital Method, AM 1 Robert J. Woods, Walter A. Szarek,* and Vedene H. Smith, Jr.* Contribution from the Department of Chemistry, Queen’s University, Kingston, Ontario, Canada K7L 3N6. Received September 15, 1989
Abstract: The AMI optimized geometries and energies of the pyranoid forms of two naturally occurring sugars, D-fructose and L-sorbose, and of the synthetic derivatives, 5-deoxy-D-rhreo-hexulose(5-deoxyfructose) and the carbocyclic analogue of Dfructose (pseudo-Dfructose), provide an explanation for the relative sweetness of these compounds. A novel approach to predicting the global energy minima of monosaccharides is presented.
D-Fructose is the sweetest of the naturally occurring sugars1 ~) and crystallizes as the 8-Ppyranose form in the e s (conformation.* Similarly, in aqueous solution 8-D-fructopyranose(1) is the preponderant species and also exists in this conformation.’ Closely related to Pfructose is its C-5 epimer, namely L-sorbose, which adopts the a-L-pyranose form and the ZC,(L) conformation in the solid state‘ and exists in aqueous solution’ almost exclusively as a-L-sorbopyranose (2). Despite the clear similarities of these two sugars, L-sorbose is markedly less sweet than bfructose.s It is generally accepted that 0-5 in 1 or 2 is not involved in binding to the sweet taste and early theorieskS6 to explain the lower sweetness of L-sorbose proposed that a hydrogen bond between HO-5 and 0-6 could exist in D-fructose and could not exist in L-sorbose. The presence of the intramolecular hydrogen bond then might be responsible for releasing HO-2 and allowing it to interact with the sweet receptor in the case of D-fructose, whereas, in the case of L-sorbose, HO-2 would be inhibited by an intramolecular hydrogen bond to 0-6. In order to test this hypothesis the hydroxyl group at C-5 was removed to generate the synthetic derivative 5-deoxy-~-threohexulose (5-deoxyfructose) (3), which exists as the ,%-pyranose form in the 2 C 5 ( ~conformation ) in aqueous solution.8 This compound was found to be much sweeter than L-sorbose and nearly as sweet as D-fructose.8 Although the form shown (see chart I) is the preponderant one for bfructose in aqueous solution, other isomers are also present, although to a lesser extent.’~~ The fructofuranoses are considered to be nearly void of sweet taste, and Shallenberger9has rationalized this property as resulting from a lack of the required steric relation between the proton donor, proton acceptor, and hydrophobic bonding sites, which were believed to comprise the saporous unit in bfructose. Of relevance is the recent observationlothat the carbocyclic analogue of &Dfructopyranose (pseudo-BD-fructopyranose,4) was found to be nearly as sweet as D-fructose;ll in contrast to Dfructose, 4 cannot mutarotate and exists only in the conformation shown. (1) Lindley, M. G.; Shallenberger, R. S.;Whistler, R. L. J. FoodSci. 1976,
41, 575-577.
(2) Takagi, S.; Jeffrey, G. A. Acta Crystallogr. 1977, B33, 3510-3515. (3) Angyal, S. J.; Bethell, G. S. Ausr. J . Chem. 1976, 29, 1249-1265. (4) Nordenson, S.;Takagi, S.;Jeffrey, G. A. Acta Crystullogr. 1979,835, 1005-1 007. (5) (a) Tsuzuki, Y.; Yamazaki, J. Biochem. Z . 1953,323,525-531. (b) Shallenberger, R. S. In Carbohydrates in Solution; Isbell, H. S., Ed.; Advances in Chemistry 117; American Chemical Society: Washington, DC, 1973; pp 256-263. (c) Birch, G. G. CRC Crirical Rev.Food Sd. Nurr. 1976, 8. 57-95. (6) Lindley, M. G.; Birch, G. G. J . Sci. Food Agr. 1975, 26, 117-124. (7) Shallenberger, R. S.;Acret, T. E. Nature 1967, 216, 480-482. (8) Martin, 0. R.; Korppi-Tommola,S.-L.;Szarek, W. A. Can. J. Chem. 1982,60, 1857-1862. (9) Shallenberger, R. S. Pure Appl. Chem. 1978, 50, 1409-1420. (IO) Suami, T.; Ogawa, S.;Takata, M.; Yashuda, K.; Takei, K.; Uematsu, Y. Chem. Loa. 1985, 719-722. (1 1) Pseudo-,9-bfructopyranosehas been reported to be somewhat sweeter than the L-enantiomer, see: Suami, T. Pure Appf. Chem. 1987, 59, 1509-1520.
Chart I &H-l
HO
OH
OH4 OH-5
& OH
S-Deoxy-P-D-1hreo-hcxuiose
12)
+2PH
OH OH
Pseudo-6-0-Fructopyranooe
(51
We have reportedL2J3earlier the results of ab initio calculations on 1 and 2 that were aimed at providing information about the electronic properties of these sugars, as part of a study concerned with a theory of sweetness. For each of these compounds, the anomeric hydroxyl group (HO-2) and 0-1 had been identified as possible proton-donating (AH) and proton-accepting (B) group, respectively; however, our results” suggest that the assignment of groups to the AH,B system in the case of 8-D-fructopyranose (1) should be reversed. Moreover, Birch et al.“ have suggested that the anomeric center of D-fructose may play no direct role in the sweet response; instead, the primary glycophore of Dfructopyranose may be the 3,4-a-glycol system. Until now no thorough study of the intramolecular interactions and their effects on the conformational preferences of hexuloses has been reported. In this paper we describe the results of such an investigation, which was undertaken in an effort to rationalize the different degrees of sweetness observed for compounds 1-4. Any calculational method used in such a study has to meet several criteria, some of which are particularly unique to carbohydrates. Not only must the method reproduce the molecular geometries to a high degree of accuracy but also it must give reasonable values for the conformational, relative energies. Furthermore, the sugar ring conformation must be reproduced, and, most importantly, the intramolecular hydrogen bonds between adjacent hydroxyl groups must be predicted accurately, both geometrically and energetically. While ab initio methods are in principle capable of meeting these requirements, it has been shown that hydrogen bonds are not well reproduced at the HartreeFock level unless a relatively (12) Szarek, W. A.; Korppi-Tommola, S.-L.;Martin, 0.R.; Smith, V. H., Jr. Can. J . Chem. 1984,62, 1506-1511. (13) Woods, R. J.; Smith, V. H., Jr.; Szarek, W. A,; Farazdel, A. J. Chem. Soc., Chem. Commun. 1987, 937-939. (14) Birch, G . G.; Shamil, S.; Shepherd, 2. Experientia 1986, 42, 1232-1 234.
QQQ2-1863/9Q/1512-4732$02.50/0 0 1990 American Chemical Society
Sweetness and intramolecular H - Bonding Networks large basis set is used in the c a l c ~ l a t i o n . ~Unfortunately, ~ since we wished to perform, and indeed found it necessary to perform, full geometry optimizations on these molecules, the amount of computing time and memory required for a b initio calculations made them impractical. However, semiempirical methodologies offer a computationally accessible approach to the evaluation of the conformational preferences of sugars.
J . Am. Chem. SOC..Vol. 112, No. 12, 1990 4133
lo -303.89
Methodology Semiempirical methods have been criticized for their poor reproductions of ring geometries; MIND0/3I6 and MND0" both underestimate the extent of the puckering in cyclohexane and related cyclic structures.'*J9 It is also accepted that each of these methodologies fails to reproduce hydrogen bond geometries and energies.mJ' However, several methods which have been claimed to perform well on hydrogen-bonded systems have been published, including MIND0/3H,22 MNDO/H,23 Goldblum's MNDO/H,U MNDO/M,= and AMI." We have recently examined two of these, namely, MNDO M and AMI, and the results of that study will be published separately) While both MNDO/M and AMI adequately predicted intermolecular hydrogen bonds in the complexations of the N-acetylamides of L-asparagine and L-serine with water, only AMI performed well in the case of the intramolecular hydrogen bonds present in B-D-fructopyranose. The primary reason for the poor performance of MNDO/M in regards to intramolecular hydrogen bonds in this case lies in the observation that MNDO/M, like its predecessor MNDO, significantly distorts the sugar ring toward planarity and creates unrealistically long hydrogen bond distances. On the basis of that preliminary work, we have performed all of the calculations in this paper by using AMI at the restricted Hartree-Fock (RHF) level, employing the keywords PRECISE and PULAY (see ref 26b), in all calculations.
Geometry Selection Carbohydrates present a unique problem to the choice of initial geometry for any calculation. The adjacent hydroxyl groups are sufficiently close to one another that each may be involved in intramolecular hydrogen bonding with its neighbor and/or possibly with the ring-oxygen atom. Furthermore, each hydroxyl group may act as a proton donor or a proton acceptor or both. Thus, in the case of hexuloses in the pyranoid form, not only do choices about the conformation of the ring have to be made but also the orientations of the hydroxymethyl and hydroxyl groups must be considered. In the case of pyranoses in the solid state, it is well-known that as many hydroxyl protons and oxygen atoms as possible are included in the hydrogen-bonding scheme;28 however, even when this aspect is taken into account, the number of possible permutations of hydroxyl-group orientations is significant. Serianni and C h i ~ m a n , in * ~a recent a b initio study of furanose ring conformations, assumed that the orientation of the anomeric hydroxyl groups (HO-2 in 1-3) (see Chart I) would be controlled by the exeanomeric effect.M We believe that this may not always
lb
-303.21
IC
-302.13
Id -301.64
le
-301.12
If -300.29
(15) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986; pp 215-223. (16) Bingham, R. C.; Dewar, M. J. S.;La,D. H. J . Am. Chem. Soc. 1975, 97. 1285-1293. (17) Dewar, M.J. S.; Thiel, W. J. Am. Chem. Soc. 1977,99,4899-4907. (18) (a) Bingham, R. C.; Dewar, M. J. S.;Lo, D. H. J . Am. Chem. Soc. 1975,97,1294-1301. (b) Felker, P.; Hayes, D. M.; Hull, L. A. Theor. Chim. Acra 1980, 55, 293-299. (19) Dewar, M. J. S.:Thiel. W. J. Am. Chem. Soc. 1977.99.4907-4917. (20) (a) Zielinski, T. J.; Breen, D. L.; Rein, R. J . Am. Chem. Soc. 1978, 100,6266-6267. (b) Klopman, G.; Andreozzi, P.;Hopfinger,A. J.; Kikuchi, 0.; Dewar, M. J. S.J. Am. Chem. Soc. 1978, 100,62674268. (21) (a) Dewar, M. J. S.;Ford, G . P. J . Am. Chem. Soc. 1979, 101, 5558-5561. (b) Scheiner, S. Theor. Chim. Acta 1980,57, 71-80. (22) Mohammad, S.;Hopfinger, A. Int. J. Quantum Chem. 1977, 22, 1189-1207. (23) (a) Burstein, K. Y.;Isaev, A. N. Theor. Chim. Acra 1984, 64, 397-401. (b) Burstein, K. Y.; Isaev, A. N. Zh. Srrukr. Khim. 1986,27,3-7. (24) Goldblum, A. J. Compur. Chem. 1987,8, 835-849. (25) Voitpk, A. A.; Bliznyuk, A. A. Theor. Chim. Acta 1987, 72, 223-228. (26) (a) Dewar, M. J. S.; Zocbisch, E. G.; Healy, E. F.; Stewart, J. J. P. J . Am. Chem. Soc. 1985,107.3902-3909. (b) The AMPAC package of com-
be the case, especially when the anomeric hydroxyl group participates in intramolecular hydrogen bonding. In order to obtain an objective and independent starting point for these calculations, we chose to define the C U H bond angles, through the use of dummy atoms, as being linear. Also, standard bond lengths and angles3' and ideal torsion angles32were employed
5297-5303.
(30) (a) Lemieux, R.U.; Koto, S.Tetrahedron 1974,30, 1933-1944. (b) Lemieux, R. U.; Koto, S.; Voisin, D. In Anomeric Effrct, Origin and Consequences; Szarek, W . A., Horton, D., Eds.; ACS Symposium Series 87; American Chemical Society: Washington, DC, 1979; pp 17-29. (31) Pople, J. A.; Gordon, M. J. Am. Chem. Soc. 1%7,89, 4253-4261. (32) "Ideal torsion angles" refers to multiples of 60°.
puter programs was employed and is available from the Quantum Chemistry Program Exchange as QCPE program No. 527. (27) Khalil, M.; Woods, R. J.; Weaver, D. F.; Smith, V. H.,Jr. J. Compur. Chem. Submitted for publication. (28) Jeffrey, G. A. In Molecular Structure and Biological Acrivity; Griffin, J. F., Duax, W. L., Eds.; Elsevier: New York, 1982; pp 135-150. (29) Serianni, A. S.;Chipman, D. M. J. Am. Chem. Soc. 1987, 109,
10
-300.22
Figure 1. AM1 optimized geometries and heats of formation of &D-
fructopyranose (1). Structures are listed in order of increasing energy.
Woods et al.
4734 J. Am. Chem. Soc., Vol. 112, No. 12, 1990 to define the ring geometry. For each starting geometry the three staggered rotamers of the hydroxymethyl group (+gauche, G+; -gauche, E,and antiperiplanar, A P 0-1 to 0-2) were included. Optimization of these idealized starting geometries consistently led to low-energy conformations exhibiting high degrees of hydrogen bonding. In fact, manipulation of the hydroxyl groups in these optimized conformations followed by reoptimization, in attempts to examine other hydrogen bond patterns, led to higher energy conformations in all but one case. This approach appears to generate global energy minima and allows for the examination of higher energy local minima.
Results A. Global Energy Minima. In our preliminary reportz7 of a comparison of the semiempirical methods MNDO/M and AM 1, we indicated that optimization of the three idealized, starting geometries of 1 gave rise to structures la, lb, and IC(see Figure 1). A more detailed discussion of the hydrogen bonds present in these conformations is now presented. Rotamers la-c differ noticeably only in the orientations of the hydroxymethyl group and, consequently, in the orientations of hydroxyl group HO- 1. In each rotamer the secondary hydroxyl groups were predicted to form similar hydrogen bonds, namely, between HO-5 and 0-6, HO-4 and 0-5, and HO-3 and 0-2. The anomeric hydroxyl group preferred to adopt the exo-anomeric orientation for all three of the rotamers. The hydrogen bond data are presented in Table I. The G+ conformation la was calculated to be the most stable structure and, in addition to hydrogen bonds between the secondary hydroxyl groups, contained hydrogen bonds between HO-1and 0-6 and HO-2 and 0-1. The energy of the G- conformation l b was found to be approximately 0.7 kcal/mol above that of la. In lb, the hydroxymethyl group adopted an orientation such that HO-1 was hydrogen bonded to 0-3, while HO-2 was hydrogen bonded to 0-1, as in la. In the third rotamer IC the hydroxymethyl group was oriented such that 0-1was AP to 0-2, and, consequently, HO-2 could no longer form a hydrogen bond to 0-1; HO-1 now formed a hydrogen bond to the ring oxygen atom, 0-6. Conformation ICwas the highest in energy, which was approximately 1.7 kcal/mol above that of la. Conformations la and l b were predicted to have the same number of hydrogen bonds, and the energy difference between them may be attributed to the fact that the G+ rotamer l a contains two stabilizing gauche effects33(between 0-1and 0-2, and between 0-1and 0-6), whereas the G rotamer l b contains only one such interaction (between 0-1and 0-2). Similarly, IC contains one gauche effect (between 0-1and 0-6); however, IC also contains one fewer hydrogen bond than does either la or lb. Optimization of the idealized starting geometries of 2 gave rise to a G+ conformation 2a, a G- conformation 2b, and an AP conformation 2c. Three hydrogen bonds were found to be common to all three rotamers of 2: between HO-5 and 0-4, HO-4 and 0-3, and HO-3 and 0-2. This pattern indicated a reversal of the hydrogen bonding involving 0 - 4 and 0 - 5 , as compared to that in 1. The hydrogen bond data for 2 are listed in Table 11. The hydroxymethyl group and hydroxyl group HO-1, in 2, adopted orientations completely analogous to those found for 1. The lowest energy rotamer was calculated to be again the G+ conformation 2a, while the G- rotamer 2b was approximately 1.2 kcal/mol higher in energy. The AP rotamer 2c was the highest energy structure, being approximately 1.7 kcal/mol higher in energy than 2a (seeFigure 2). As in 1, hydroxyl group H0-2, in 2, was found to prefer the exo-anomeric orientation in each of the three lowenergy structures. In 3, the 5deoxy analogue of 1 and 2, the possibility of hydrogen bonding involving 0-4 and 0 - 5 does not exist, and optimization of the idealized rotamers of 3 gave rise to the low-energy conformers 3%3b, and 3c. The hydrogen bond data for 3 are given in Table 111. These conformers were found to exhibit hydrogen bonding between HO-4 and 0 - 3 and between HO-3and 0-2, (33) (a) Wolfe, S.; Rauk, A.; Tel. L. M.;Csizmadia, I. G. J. Chem. Soc. B 1971, 136-145. (b) Kirby, A. J. The Anomeric Eflect and Related Stereoelectronic Effrctsat Oxygrn: Springer-Verlag: New Yo& 1983; pp 32-36.
Table I. Hydrogen Bond Distances (A) and Angles (deg) for the AM1 Optimized Geometries of 8-D-Fructopyranose (1) conformation (heat of formation)" D-H-A D-H D--A H-A LDHA
la (-303.89) 0-1-HO-1.**0-6 0.967 0-2-HO-2**.0-1 0.969 0-3-HO-3***0-2 0.967 0-4-HO-4.**0-5 0.968 0-5-HO-5*.*0-6 0.967 mean values 0.967
2.820 2.784 2.786 2.805 2.939 2.827
2.491 2.275 2.472 2.354 2.490 2.416
99.73 1 1 1.78 98.63 107.76 108.22 105.23
0-1-HO-1..*0-3 0-2-HO-2..*0-1 0-3-HO-3*..0-2 0-4-HO-4*.*0-5 0-5-HO-5.**0-6 mean values
0.969 0.967 0.968 0.968 0.967 0.968
3.056 2.614 2.746 2.805 2.940 2.832
2.357 2.360 2.473 2.343 2.486 2.404
128.56 94.14 95.87 108.47 108.59 107.13
0-1-HO-1...0-6 0-3-HO-3**.0-2 0-4-HO-4...0-5 0-5-HO-5*.*0-6 mean values
0.967 0.967 0.968 0.967 0.967
2.699 2.747 2.816 2.930 2.798
2.331 2.425 2.377 2.488 2.405
101.72 98.96 106.98 107.64 103.82
0-1-HO-1..*0-3 0.969 0-3-HO-3*.*0-2 0.967 0-4-HO-4***0-5 0.968 0-5-HO-5*..0-6 0.967 mean values 0.968
2.860 2.773 2.818 2.944 2.849
2.229 2.481 2.370 2.496 2.394
121.75 97.18 107.59 108.12 108.66
0-1-HO-1*..0-6 0-2-HO-2-.0-3 0-3-HO-3..*0-4 0-4-HO-4...0-5 0-5-HO-5-*0-6 mean values
0.966 0.967 0.967 0.968 0.968 0.967
2.702 2.741 2.934 2.798 2.904 2.816
2.355 2.248 2.499 2.298 2.446 2.369
100.38 110.52 107.14 1 1 1.19 108.64 107.58
0-1-HO-1..*0-3 0-2-HO-2.**0-3 0-3-HO-3.*.0-4 0-4-HO-4*..0-5 0-5-HO-5**.0-6 mean values
0.968 0.967 0.967 0.969 0.967 0.968
2.819 2.781 2.908 2.798 2.936 2.849
2.217 2.302 2.461 2.293 2.482 2.351
119.24 109.73 107.92 1 1 1.56 108.50 1 1 1.39
0-1-HO-1**.0-2 0.968 0-2-0H-2...0-3 0.967 0 - 3 - H O - 3 4 - 4 0.968 0-4-HO-4.*.0-5 0.969 0-5-HO-5***0-6 0.967 mean values 0.968 a Energies are in kcal/mol.
2.767 2.778 2.910 2.801 2.934 2.838
2.239 2.288 2.457 2.296 2.474 2.351
113.15 110.46 108.32 1 1 1.54 108.97 110.49
lb (-303.21)
lc (-302.13)
Id (-301.64)
le (-301.12)
If (-300.29)
1g
(-300.22)
analogously to that found for the low-energy conformers of 2. Hydrogen bonds involving the hydroxymethyl group in each of the G+ (3a). G- (3b), and AP (3c) rotamers were generated between HO-1 and 0-6, HO-1 and 0-3, and HO-1 and 0-6 respectively. In each of these rotamers, the anomeric hydroxyl group, HO-2, preferred the exo-anomeric orientation, with the lowest energy structure being 3a, followed by 3b,which was 1.1 kcal/mol higher in energy, and then 3c,whose energy was 1.8 kcal/mol above that of 3a (see Figure 3). In the case of pseudosugar 4, structures 4g, 4c, and 4n,corresponding to the G+, G-, and AP rotamers, respectively, were generated by optimization of the idealized starting geometries. These were not the lowest energy conformations found for this molecule. Manipulation of the hydroxyl group orientations in 4g, 4c, and 4n, followed by full geometry optimization, indicated that there were several stable orientations for each hydroxyl group, many of which differed in energy by less than 0.5 kcal/mol (see
Sweetness and Intramolecular
J. Am. Chem. Soc., Vol. 112, No. 12. 1990 4135
H-Bonding Networks
29 -298.38
20
-303.56
U
2h
Zb
-298.27
-302.36
2i
2c
-297.62
-301.82
a 2d
-300.89
2e
-300.11
2f
-299.47
Zj -297.12
2k
-296.74
21
-296.37
Figure 2. AMI optimized geometries and heats of formation of a-L-sorbopyranose (2). Structures are listed in order of increasing energy.
Figure 4). In 4, hydroxyl group HO-2 no longer has the electronic and structural properties associated with an anomeric hydroxyl groupM and may be expected to have properties similar to those and HO-5. This of the secondary hydroxyl groups HO-3, HO-4, structural aspect appeared to have the effect of lowering the energy differences between conformations in which 0-1,0-2, and 0 - 3 were involved in intramolecular hydrogen bonding. Furthermore, replacement of the ring-oxygen atom by a methylene group removed the stabilizing gauche interaction in the AP rotamer, a situation which would destabilize such rotamers as compared to G+ and G structures. The subtle geometrical differences between the cyclohexyl and pyranoid ring systems were reflected in the average 0-0 distance between vicinal hydroxyl groups. On the basis of all of the conformations of 4 this distance was 2.805 A; the corresponding value based on all of the conformations of structures 1-3 was 2.828 A. The shorter 0-0 separations in 4 had the effect of increasing further the number of stable hydroxyl-group orientations in the case of 4 relative to the numbers
in the cases of 1,2, and 3. Thus, for 4 optimization of the idealized geometries did not lead to global energy minima. Despite the differing configurations at C-5 among compounds 1-3, in all cases the analogous rotamers resulting from the optimization of the idealized geometries were predicted to have the same hydrogen bond patterns involving 0-1,O-2, and 0 - 3 . No significant differences in either the relative stabilities or geometries of the rotamers were found. Since 0-1 and 0 - 2 in each of 1-3 are believed** to be involved in the interaction with the sweet receptor, we concluded that the low sweetness of 2 relative to that of 1 or 3 is attributable presumably to conformations of these molecules of higher energy than those found by the optimization of the idealized geometries. The single notable difference between 1 and 2 was found to be in the behavior of HO-4. In 1, HO-4 consistently preferred to form a hydrogen bond with 0 - 5 , rather than with 0 - 3 , and, hence, in 1, HO-3 might be able to form a hydrogen bond with 0-4, a process requiring the breaking of only a hydrogen bond
4136
Woods et al.
J . Am. Chem. SOC.,Vol. 112, No. 12, 1990
3a
31
-259.44
-254.59
3b
3fb
-258.31
-254.43
3c
3j
-257.64
-254.42
3d
3k
-256.74
-254.33
3s
31
-256.00
-254.24
3f a -255.53
3g -255.37
3m -254. 16
3n
-252.86
3h
30
-255.36
-252.48
Figure 3. AMI optimized geometries and heats of formation of 5-deoxy-~-rhreo-hexulose (3). Structures are listed in order of increasing energy.
Sweetness and Intramolecular H - Bonding Networks
4a
-268.31
4b
-267.74
4c
-267.68
4d
-267.65
40
-266.84
4c
-266.77
48
-266.62
J . Am. Chem. SOC.,Vol. 112, No. 12, 1990 4131
4h
-265.93
41
-265.82
4J
-265.28
4k
-265.12
41
-264.23
4m
-263.54
4n
-263.23
Figure 4. AMI optimized geometries and heats of formation of pseudo$-o-fructopyranose (4). Structures are listed in order of increasing energy.
between HO-3 and 0-2. In such a case 0 - 3 would be free to act as a hydrogen bond acceptor for HO-1 or HO-2 and, thus, could alter the preferred, low-energy orientation of HO-1 or HO-2. However, in 2, HO-4 consistently formed a hydrogen bond with 0-3, and, consequently, in 2, HO-3 might not be able to form a hydrogen bond with 0-4, in which case 0 - 3 could not act as a hydrogen bond acceptor for HO-1or HO-2. Thus, there might be higher energy conformations of 1 and 2 in which the orientations of HO-1 and HO-2 were not analogous, an aspect which
might rationalize, at least partly, the gustatory differences between 1 and 2. To test this hypothesis all of the possible permutations of hydrogen bonds among the hydroxyl groups of each rotamer of 1 4 were generated and fully optimized (see Figures 1 4 ) . The starting geometries were chosen so as to maximize the number of intramolecular hydrogen bonds. In several cases different starting geometries collapsed to the same final geometry. B. Local Energy Minima. No stable conformations of 1 were found in which HO-4 acted as an hydrogen bond donor in a
Woods et al.
4138 J. Am. Chem. Soc., Vol. 112, No. 12, 1990 Table 11. Hydrogen Bond Distances
conformation (heat of formation)0
(A) and Angles (deg) for the AM1 Optimized Geometries of a-L-Sorbopyranose (2)
D-H-aA
D-H D--A H--A LDHA
conformation (heat of formationy
D-H.-A
D-H D.-A
H--A LDHA
0-1-HO-1*..0-6 0-4-HO-4*-0-3 0-5-HO-5*..0-4 mean values
0.967 0.967 0.967 0.967
2.851 2.845 2.852 2.850
2.485 2.449 2.420 2.451
102.28 104.22 106.72 104.41
0-1-HO-14-6 0-2-HO-2.4-3 0-4-HO-44-3 0-5-HO-5***0-4 mean values
0.967 0.966 0.967 0.967 0.967
2.806 2.777 2.896 2.861 2.835
2.450 2.496 2.514 2.457 2.479
101.40 96.56 103.48 104.80 101.56
0-1-HO-1*.*0-2 0-1-HO-1...0-3 0-2-HO-2*-0-1 0-3-HO-3.**0-4 0-5-HO-5-44 mean values
0.969 0.969 0.968 0.966 0.967 0.968
2.603 3.105 2.603 2.938 2.864 2.823
2.595 2.425 2.322 2.589 2.454 2.477
79.77 126.96 95.76 101.48 105.19 101.83
0-1-HO-1*.*0-3 0-2-HO-2*.*0-3 0-3-HO-3-0-4 0-4-HO-4...0-5 mean values
0.967 0.966 0.967 0.967 0.967
2.791 2.777 2.867 2.857 2.823
2.192 2.290 2.458 2.432 2.343
118.82 110.27 105.18 106.20 110.12
0-1-HO-1*..0-3 0-3-HO-3-.*0-4 0-4-HO-4.*.0-5 mean values
0.968 0.967 0.966 0.967
2.745 2.851 2.859 2.818
2.150 2.407 2.462 2.340
118.32 107.49 104.29 110.04
0-1-HO-1.**0-2 0-2-HO-2***0-3 0-4-HO-4**.0-3 0-5-HO-54-4 mean values
0.968 0.966 0.966 0.967 0.967
2.751 2.794 2.897 2.859 2.825
2.226 2.281 2.538 2.458 2.376
112.92 112.26 101.98 104.58 107.93
21
(-298.38)
(-303.56) 0-1-HO-1***0-6 0.967 0-2-HO-2*..0-1 0.968 0-3-HO-3***0-2 0.968 0-4-HO-4.**0-3 0,967 0-5-HO-5...0-4 0.967 mean values 0.967
2.810 2.786 2.762 2.924 2.849 2.826
2.478 2.290 2.322 2.492 2.421 2.401
99.84 110.88 106.75 106.95 106.38 106.16
2b
(-298.27)
2b
(-302.36) 0-1-HO-1*..0-3 0-2-HO-2***0-1 0-3-HO-3--0-2 0-4-HO-4-.0-3 0-5-HO-5*-0-4 mean values
0.968 0.967 0.969 0.966 0.967 0.967
3.100 2.616 2.714 2.956 2.852 2.847
2.401 2.400 2.302 2.539 2.430 2.414
128.70 91.81 104.69 106.06 105.93 107.44
0-1-HO-1*.*0-6 0-3-HO-3...0-2 0-4-HO-4***0-3 0-5-HO-5.4-4 mean values
0.967 0.968 0.967 0.967 0.967
2.742 2.743 2.927 2.847 2.815
2.350 2.314 2.486 2.418 2.392
103.48 105.95 107.62 106.40 105.86
2i
(-297.62)
2c
(-301.82)
2i
(-297.1 2)
M (-300.89) O-I-HO-1...0-3 0-3-HO-3-*0-2 0-4-HO-4...0-3 0-5-HO-5...0-4 mean values
0.968 0.968 0.967 0.967 0.967
2.851 2.739 2.932 2.848 2.843
2.230 2.326 2.494 2.426 2.369
120.89 104.90 107.36 106.01 109.79
2k (-296.74)
b (-300.1 1) 0-1-HO-1...0-2 0-2-HO-2**.0-3 0-3-HO-3*..0-1 0-4-HO-4-*0-3 0-5-HO-5...0-4 mean values
0.968 0.965 0.969 0.967 0.967 0.967
2.701 2.745 2.916 2.915 2.863 2.828
2.337 2.51 1 2.177 2.538 2.459 2.404
101.45 93.50 132.06 103.20 104.81 107.00
0-1-HO-1*.*0-2 0-3-HO-3..*0-1 0-4-HO-4*-0-3 0-5-HO-54-4 mean values E Energies are in kcal/mol.
0.968 0.968 0.967 0.967 0.967
2.772 2.905 2.852 2.850 2.844
2.339 2.156 2.457 2.415 2.342
106.34 133.09 104.17 106.81 112.60
2f
(-299.47)
hydrogen bond with 0-3, either with or without a hydrogen bond between HO-5 and 0-4. In all cases, upon optimization, the hydroxyl groups in 1 rotated so as to generate hydrogen bonds between HO-4 and 0 - 5 and between HO-5 and 0-6. In several cases, attempts to find stable ‘anti-e~o-anomeric”~‘orientations of HO-2 yielded only the orientations preferred by the exoanomeric effect. The presence of the anti-exo-anomeric orientation of HO-2 in structures le-g indicated that this orientation existed by virtue of a hydrogen bond between HO-2 and 0-3. In these structures 0-4 acted as a proton acceptor in a hydrogen bond with HO-3. Further stabilization for the anti-exo-anomeric orientation of HO-2, in the G+ rotamer lg, was provided through the formation of a hydrogen bond between HO-1 and 0-2. The anti-exo-anomeric conformations, le, If, and lg, are a p proximately 1 .O, 1.4, and 3.7 kcal/mol higher in energy than the corresponding exo-anomeric rotamers, IC, Id, and la, respectively. A comparison of the energies of IC and l e and of Id and l f indicated that a destabilization corresponding to only 1-1.5 kcal/mol occurred when HO-2 adopted the anti-exo-anomeric orientation. A comparison of ICand Id led to an estimate of 0.5 kcal/mol as the energy lost in the breaking of a hydrogen bond (34) The term ‘anti-exo-anomeric” is used to indicate that the anomeric hydroxyl proton (HO-2) adopts a torsion angle with respea to the ring-oxygen atom (0-6) of approximately 180°, as compared to the exo-anomericorientation, in which this torsion angle is approximately 60°.
21
(-296.37)
between HO-1 and the ring-oxygen atom, 0-6, and the forming of one between HO-1 and 0-3. Of the conformations calculated for 2, all but 2j and 2k exhibited a preference for the formation of hydrogen bonds between HO-5 and 0 - 4 and between HO-4 and 0-3. This reversal of the hydrogen bond pattern in 2j and 2k resulted in a destabilization of these conformations by approximately 4 kcal/mol, as compared to the corresponding low-energy rotamer 2d. The AP rotamers, 2c and M ,differed by approximately 1 kcal/mol, a feature which represents the net destabilization induced by the breaking of a hydrogen bond between HO-1 and 0 - 6 in the case of 2c and the forming of one between HO-1 and 0 - 3 in the case of 2d. This energy difference was larger than that calculated for a similar reorganization of hydrogen bonds in 1 and may be reflective of the fact that in Id 0-3 may be able to function more effectively as a hydrogen bond acceptor with HO-1 than it may in 2d. Four conformers of 2 were found in which the anomeric hydroxyl group, HO-2, did not exist in the exo-anomeric Orientation, namely, 2e,a,2j, and 21. Conformers 2e and 21 were generated from the G- and G+ rotamers of the hydroxymethyl group, respectively, while in conformers 2h and 2j the hydroxymethyl group adopts an AF’orientation. The torsion angles between atoms H0-2-0-24-2-0-6 in 2e, 2b, and 2l were unusually small, having an average value of 113’ as compared to 164O for conformers leg. This angular distortion may be due, in part, to a repulsive
J . Am. Chem. SOC.,Vol. 112, No. 12, 1990 4739
Sweetness and Intramolecular H - Bonding Networks Table 111. Hydrogen Bond Distances
conformation (heat of formation)a 3a (-259.44)
(A) and Angles (deg) for the AM1 Optimized Geometries of 5-Deoxy-8-~-rhreo-hexulose (3)
D-H--A
D-H
D-A
H-A
LDHA
0-1-HO-14-6 0-2-HO-2.*.0-1 0-3-HO-3*-0-2 0-4-HO-4.-0-3 mean values
0.967 0.968 0.968 0.967 0.967
2.804 2.789 2.762 2.916 2.818
2.467 2.293 2.325 2.469 2.389
100.15 110.87 106.60 107.91 106.38
conformation (heat of formation)# % (-255.37)
D-H-A
D-H
De-A H..A
LDHA
0.968 0.968 0.967 0.968
2.769 2.901 2.842 2.837
2.325 2.163 2.432 2.307
107.12 131.90 105.10 114.71
0-1-HO-1*..0-6 0.967 0-2-HO-2*.*0-3 0.967 0-3-HO-3***0-4 0.967 mean values 0.967
2.731 2.751 2.914 2.799
2.354 2.267 2.460 2.360
102.46 109.94 108.44 106.95
0-1-HO-1..*0-3 0-2-HO-2.*.0-1 0-2-HO-2...0-3 0-3-HO-3-.0-4 mean values
0.968 0.968 0.968 0.967 0.968
2.855 2.754 2.818 2.853 2.827
2.179 2.217 2.772 2.41 1 2.395
125.78 113.85 82.72 107.38 107.43
0-1-HO-1.**0-2 0-2-HO-2..*0-3 0-3-HO-3*.*0-4 mean values
0.968 0.967 0.968 0.968
2.773 2.768 2.904 2.815
2.235 2.284 2.437 2.319
113.97 110.02 109.32 111.10
0-1-HO-1*..0-3 0-2-HO-2.**0-3 0-3-HO-3.*.0-4 mean values
0.967 0.966 0.967 0.967
2.790 2.764 2.902 2.819
2.195 2.285 2.445 2.308
118.57 109.69 108.56 112.27
0-1-HO-1*..0-2 0-3-HO-3.**0-1 0-4-HO-4-*0-3 mean values 3b
(-255.36)
3b
(-258.3 1) 0-1-HO-1.*.0-3 0-2-HO-2*.*0-1 0-3-HO-3**.0-2 0-4-HO-4*-0-3 mean values
0.968 0.966 0.968 0.967 0.967
3.092 2.617 2.717 2.939 2.841
2.388 2.406 2.308 2.502 2.401
129.16 91.56 104.44 107.32 108.12
3i
(-254.59)
3c (-257.64) 0-1-HO-1*.*0-6 0-3-HO-3*-0-2 O+HO-4***0-3 mean values
0.967 0.967 0.967 0.967
2.742 2.745 2.916 2.801
2.341 2.319 2.459 2.373
104.13 105.78 108.68 106.19
3j
(-254.42)
3d (-256.74)
0-1-HO-1*..0-3 0.968 0-3-HO-3***0-2 0.967 0-4-HO-4***0-3 0.967 mean values 0.968
2.852 2.739 2.919 2.837
2.222 2.329 2.465 2.339
121.63 104.68 108.49 11 1.60
0-1-HO-1--*0-2 0.968 0-2-HO-2*.*0-3 0.965 0-3-HO-3...0-1 0.969 0-4-HO-4***0-3 0.967 mean values 0.967
2.705 2.745 2.906 2.897 2.813
2.335 2.493 2.172 2.501 2.375
101.82 94.61 131.44 104.43 108.07
3e (-256.00)
3k (-254.33)
31
(-254.24) 0-1-HO-1***0-6 0.967 2.850 2.472 103.04 0-4-HO-4.**0-3 0.967 2.831 2.422 105.02 mean values 0.967 2.840 2.447 104.03
3fa
(-255.5 3) 0-1-HO-1...0-2 0.967 0-1-HO-1***0-6 0.967 0-2-HO-2*-0-1 0.967 0-2-HO-2-0-3 0.967 0-3-HO-3***0-4 0.968 mean values 0.967
2.579 3.128 2.579 2.808 2.894 2.798
2.476 85.01 2.822 99.34 2.426 87.89 2.577 93.53 2.406 110.72 2.541 95.30
0-1-HO-1.-0-2 0.967 0-1-HO-1.-0-6 0.967 0-2-HO-2***0-1 0.967 0-2-HO-2-.0-3 0.967 0-3-HO-3**.0-4 0.967 mean values 0.967
2.576 3.130 2.576 2.798 2.854 2.787
2.463 85.62 2.823 99.39 2.452 86.23 2.541 95.10 2.423 106.64 2.540 94.60
3m
(-254.16) 0-1-HO-1**.0-6 0-2-HO-2.**0-3 0-4-HO-4..*0-3 mean values
3fi
(-254.43)
2.830 2.802 2.885 2.839
2.471 2.322 2.489 2.427
101.71 109.84 104.33 105.29
30
(-252.86) 0-1-HO-1.**0-3 0.968 2.772 2.157 120.06 0-3-HO-3***0-4 0.967 2.837 2.389 107.71 mean values 0.968 2.804 2.273 11 3.89 30 (-252.49)
0-1-HO-1*.*0-2 0-2-HO-2*.*0-3 0-4-HO-4...0-3 mean values a
0.967 0.967 0.967 0.967
0.968 0.966 0.966 0.967
2.758 2.800 2.880 2.813
2.224 2.270 2.500 2.331
113.62 113.52 103.25 110.13
Energies are in kcal/mol.
interaction between HO-2 and HO-3 in the case of 2,despite the presence of a hydrogen bond between HO-2 and 0-3. An examination of 2e, in which 0-1adopted the G- orientation, indicated that hydrogen bonding between HO-1 and 0 - 2 generated the most distorted torsion angle (103'). while in 21, in which 0-1 adopted the G+ orientation, the torsion angle was the least distorted (136'). The relative energies of 2e, 2h, 2j, and 21,when compared to the energies corresponding low-energy exeanomeric rotamers, 2b,2c, 2d, and 2a,were found to be 2.2, 3.5, 3.8, and 7.2 kcal/mol, respectively. The fraction of the energy responsible for the destabilization of conformers 29,2b,and 2k attributable to the absence of an exo-anomeric effect may be compensated for by the stabilization gained through the formation of a hydrogen bond between HO-2 and 0-3. This hypothesis is supported by the observation that there is a small energy difference between rotamers 2g and 2h,which differ only in the orientation of HO-2. Moreover, conformer 2j, in which HO-2 adopts an anti-exoanomeric orientation, is approximately 0.4 kcal/mol more stable than the corresponding exo-anomeric rotamer 2k. Thus, most of
the destabilization of the conformers of 2 having the anti-exoanomeric orientations may arise from the reorganization of hydrogen bonds between 0 - 2 , 0-3, and 0 - 4 in these conformers. On the basis of the above results, the observation that 1 and 2 differed in the nature of the interaction between HO-4 and 0 - 3 may be further generalized. In 1 the ability of HO-4 to act as a hydrogen bond acceptor translated into a stabilization of conformations containing hydrogen bonds between HO-3 and 0-4. This feature in turn allowed HO-2 to adopt anti-exo-anomeric orientations that were stabilized by hydrogen bonding between HO-2 and 0-3. However, in 2, the preference of HO-4 to act as a proton donor in a hydrogen bond with 0 - 3 limited the ability of 0 - 3 to act as a proton acceptor in a hydrogen bond with HO-2. While stable conformations of 2 were found in which HO-2 was hydrogen bonded to 0-3, they were less stable energetically than similar conformations of 1. Removal of the hydroxyl group at C-5 in either 1 or 2 generates the sweet, synthetic deoxy sugar 3. Since 3 is closely related to both 1 and 2,it might be expected to adopt conformations present
Woods et al.
4140 J. Am, Chem. Sa.,Vol. 112, No. 12, 1990
Table IV. Hydrogen Bond Distances (A) and Angles (deg) for the AMI Optimized Geometries of Pscudo-&wFructopyranosc (4) conformation con formation (heat of formation)' D-H-aA D-H D-A H--A LDHA (heat of formation)' D-H..A D-H H . 4 LDHA
4a (-268.3 I )
4g
(-266.62)
0.967 0.969 0.969 0.968 0.968 0.968
2.792 2.728 2.799 2.826 2.797 2.788
2.128 2.251 2.51 1 2.320 2.292 2.300
O-l-HO-l...O-2 0.967 0-2-HO-2***0-3 0.968 0-3-HO-3**.0-4 0.968 0-4-HO-4.-0-5 0.968 mean values 0.968
2.780 2.768 2.840 2.793 2.795
2.303 109.51 2.286 2.347 110.89 2.284 2.305 110.50
0-1-HO-14-3 0-2-HO-24-1 0-2-HO-2-0-3 0-3-HO-3..*0-4 0-4-HO-4**.0-5 mean values
124.44 109.18 96.97 1 1 1.78 11 1.63 110.80
4b
123.62 115.50 87.90 81.37
0-1-HO-1...0-3 0-2-HO-2...0-1 0-3-HO-3-0-2 0-4-HO-4-*0-3 0-5-HO-5*.*0-4 mean values
0.968 0.968 0.968 0.967 0.967 0.967
2.810 2.733 2.773 2.868 2.771 2.791
2.167 2.195 2.351 2.393 2.324 2.286
122.72 113.85 105.64 109.74 107.38 111.87
0-2-HO-2.**0-1 0-3-HO-3-0-2 0-4-HO-4..*0-3 0-5-HO-5.*.0-4 mean values
0.967 0.968 0.967 0.967 0.967
2.770 2.766 2.853 2.768 2.789
2.251 2.309 2.373 2.314 2.312
112.50 107.99 110.04 107.86 109.60
0-2-HO-2*..0-1 0-3-HO-34-2 0-4-HO-4*-0-5 mean values
0.968 0.967 0.967 0.967
2.771 2.775 2.805 2.784
2.240 113.38 2.439 99.97 2.364 107.07 2.348 106.81
0-2-HO-2-0-3 0-3-HO-3..*0-4 0-4-HO-44-5 mean values
0.968 0.967 0.968 0.968
2.752 2.846 2.793 2.797
2.280 2.367 2.289 2.312
0-1-HO-1..*0-3 0-3-HO-34-2 0-4-HO-4***0-5 mean values
0.968 0.967 0.968 0.967
3.018 2.814 2.797 2.876
2.407 120.73 2.522 97.31 2.349 107.58 2.426 108.54
0-1-HO-1.*.0-3 0-3-HO-34-2 0-4-HO-4***0-3 0-5-HO-5**.0-4 mean values
0.968 0.967 0.967 0.967 0.967
2.977 2.801 2.852 2.762 2.848
2.329 2.372 2.361 2.302 2.341
123.69 106.24 110.82 108.28 112.26
0-3-HO-3.-0-2 0-4-HO-4***0-3 0-5-HO-5..*0-4 mean values
0.967 0.967 0.967 0.967
2.752 2.859 2.766 2.792
2.303 2.376 2.300 2.326
107.42 110.29 108.68 108.79
109.04 109.98 11 1.51 110.18
(-265.28)
103.30
4d (-267.65)
4k (-265.12)
4e 41
41
(-264.23)
4m
(-266.77) 0-1-H0-1.-0-3 0-2-HO-2-0-3 0-3-HO-3.**0-4 0-4-HO-4...0-5 mean values
0.967 0.967 0.968 0.968 0.968
2.934 2.809 2.832 2.796 2.843
2.323 2.356 2.330 2.290 2.325
120.46 107.98 111.51 1 1 1.70 112.91
(-263.54) 0-3-HO-3***0-2 0.967 2.755 2.430 99.23 0-4-HO-4*.*0-5 0.967 2.809 2.377 106.47 mean values 0.967 2.782 2.403 102.85
4n (-263.23) 0-2-HO-2-0-3 0-3-HO-34-4 0-5-HO-54-4 mean values
a
109.82 109.74 110.73 108.03 109.58
4j
108.10
(-266.84)
2.297 2.287 2.356 2.315 2.314
(-265.82)
(-267.68) 2.120 2.180 2.705 2.81 1 2.362 2.445
2.779 2.768 2.846 2.771 2.791
4i
4c
2.776 2.740 2.839 2.832 2.817 2.800
0.967 0.967 0.967 0.967 0.967
4b (-265.93)
(-267.74)
0-1-HO-14-3 0.968 0-2-HO-2..*0-1 0.969 0-3-HO-3***0-2 0.966 0-3-HO-3*-0-4 0.966 0-4-HO-4.**0-5 0.968 mean values 0.967
0-1-HO-1.*.0-2 0-2-H0-2.-0-3 0-3-HO-3.4-4 0-4-HO-4.*0-5 mean values
0.968 0.967 0.964 0.966
2.756 2.876 2.813 2.815
2.293 108.38 2.411 109.14 2.663 88.83 2.456 102.12
Energies are in kcal/mol.
in both 1 and 2. This aspect was indeed found to be the case. The hydrogen bond found between HO-4 and 0-3 in 3 was similar to the hydrogen bonds observed in the rotamers of 2 corresponding to the global energy minima. However, unlike the conformations found for 2, low-energy conformations of 3 were found (3e,3f, 3h-k) in which the anomeric hydroxyl group adopted the antiexo-anomeric orientation. These conformations were stabilized by the presence of a hydrogen bond between HO-2 and 0-3 in a manner completely analogous to that Seen for both 1 and 2. The relative energies of these anti-exo-anomeric conformers were in the region 2.2-3.9 kcal/mol above those of the corresponding exo-anomeric rotamers. Furthermore, the anti-exo-anomeric conformer 3e is approximately 0.6 kcal/mol more stable than the analogous exo-anomeric conformer 3g. It appeared that, without the influence of an hydroxyl group at C-5, the hydrogen bonding between HO-4 and 0 - 3 could be readily reorganized so as to allow the formation of an hydrogen bond between HO-2 and 0-3.35 In those conformations of 3 in
which 0 - 4 acted as an acceptor atom in an hydrogen bond with HO-3, HO-4 adopted two stable orientations, for example, see 3fa and 3fb. These conformers differ in energy by approximately 1.1 kcal/mol, a value representing the difference in energy between tetrahedral and planar, hydrogen bond coordination to 0-4. Although both of these types of coordination have been shown *~' to be statistically, equally likely in the solid ~ t a t e , ~gas-phase results indicate a preference for tetrahedral coordination.'* In the anti-exo-anomeric rotamers 3fa, 3h, 3j, and 3k, tetrahedral coordination to 0 - 4 was calculated to be more stable than planar coordination by an average value of 1.2 kcal/mol, whereas, planar coordination to 0-4 was preferred for the exo-anomeric rotamers 3i and 3n. The presence of stable conformations of 3 in which HO-2 adopts an anti-exo-anomeric orientation, having relative energies similar to those found for 1, suggested that an anti-exo-anomeric orientation of HO-2 may be pertinent to the sweetness of hexuloses. In the case of 4, the results of the optimizations may be summarized as follows. Hydrogen bonding between HO-4 and 0 - 5
(35) This rcor&zation might be expected to require leas energy than was required in the caw of 2 on the basis that the stabilization due to the coop erative effect in 3 would be smaller than in 2 (see ref 28).
(36) Vedani, A.; Dunitz, J. D. 1.Am. Chem. Soc. 1985,107,7653-7658. (37) Taylor, R.; Kennard, 0. Acc. Chem. Res. 1984, 17, 320-326. (38) Millen, D. J. Crwr. Chem. Rcru 1982, 55, 133-145.
J . Am. Chem. SOC.1990, 112,4141-4141 may involve either tetrahedral or planar coordination to 0-5,the former usually being preferred by approximately 1.1 kcal/mol. When a hydrogen bond was present between HO-4 and 0-5, hydroxyl group HO-2 adopted an "anti-exo-an~meric"~~ orientation, thereby generating a chain of hydrogen bonds extending between HO-2 and 0-3, H0-3 and 0-4, and H0-4 and 0 - 5 . This hydrogen bond pattern led to the lowest energy structures. Alternatively, when HO-5 formed a hydrogen bond with 0-4, a network of hydrogen bonds was generated between HO-5 and 0-4, HO-4 and 0-3, and HO-3 and 0-2. This latter situation was less stable (by approximately 1 kcal/mol) than the former pattern and required that HO-2 adopt the "exo-anomeric" orientation. In the high-energy structure 4n, 0-4 acted as a proton acceptor in hydrogen bonds with both HO-5 and HO-3, generating a three-center hydrogen bond.
Conclusions The differences between the conformational preferences of 4 and 1-3 arise primarily from two factors. Firstly, replacement of 0-6 by a methylene group subtly alters the ring geometry, and, secondly, the absence of the exo-anomeric effect changes the geometrical preferences of HO-2. In 4 the preference for HO-2 to adopt an 'anti-exo-anomeric" orientation is attributable to the lack of an exo-anomeric effect as well as to the presence of an (39) In a pseudosugar there is no ring-oxygen atom, and the terms antiexo-anomeric and exo-anomeric are used simply for case of comparison between 4 and the other structures.
4741
interaction between HO-2 and 0-3. In each of the sweet compounds, 1,3, and 4, low-energy conformations were found to exist in which HO-2 was hydrogen bonded to 0-3. This anti-exo-anomeric orientation of H0-2 was less favored energetically in the case of the less sweet sugar 2. While hydroxyl group HO-2 traditionally is believed to act as a proton donor in a hydrogen bond with the sweet receptor, previous work by us13 has suggested that HO-2 may function as a proton acceptor (seealso ref 40). As such, it must be capable of adopting orientations in which the hydroxyl proton is directed away from the proton-donor functionality of the receptor. On the basis of the geometry of the tripartite r e ~ e p t o r , ~HO-2 ' might act most effectively as a proton acceptor when it adopts an anti-exoanomeric orientation. Thus, the ability of HO-2 to adopt an anti-exo-anomeric orientation may be related to the strength of the binding between the sweet molecule and the sweet receptor, and hence, may be pertinent to the sweetness of the molecule.
Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for the award of grants (to W.A.S. and V.H.S.) and a scholarship (to R.J.W.). Registry NO. 1,766@25-5; 2,470-15-5; 3,82945-01-5; 4,115225-55-3. (40) Woods, R. J.; Khalil, M.; Pell, W.; Moffat, S. H.; Smith, V. H., Jr. J. Comput. Chcm. 1990, 11, 297-3 10. (41) (a) Kier, L. B. J . Pharm. Sei. 1972, 61, 1394-1397. (b) Shallenberger, R. S.;Lindley, M. G. Food Chem. 1977, 2, 145-153.
Atomic Polarizability and Electronegativity Jeffrey K. Nagle Contribution from the Department of Chemistry, Bowdoin College, Brumwick, Maine 0401 I. Received October 26, 1989
Abstract: A close relationship between atomic polarizability and electronegativity is demonstrated. It is shown how atomic polarizability can be used in conjunction with the number of s and p valence electrons to derive electronegativities interpreted as either valence electton densities or the electrostatic force exerted on valence electrons. This leads to a new set of electronegativities for every element in the periodic table that can be easily calculated and understood. Such values are in substantially better agreement with traditional Pauling values than those derived as the average of ionization energy and electron affinity. It is further demonstrated that traditional or chemical electronegativities are more closely related to the density functional definition of hardness than to the corresponding definition of electronegativity. This approach offers promise to ongoing theoretical efforts to delineate the role of electronegativity in chemical bonding.
The concept of electronegativity as first proposed by Pauling has become an indispensible tool for all chemists and is also used in physics, biology, and geology.' Despite the many variations and extensions of this basic idea, Pauling's original definition as 'the power of an atom in a molecule to attract electrons to itself"lf continues to find widespread acceptance. Even the actual numerical values are still widely used and cited.' ( I ) (a) Electroncgcniuity; Sen, K. D., Jorgensen, C. K.,W.; SpringerVerlag: New York, 1987; Structure and Bonding, Vol. 66. (b) Pauling. L.; Herman, 2.S. In Moleculur Structure und Energetics; Liehman, J. F., Greenberg, A., Eds.; VCH: Deerfield Beach, FL, 1986; Vol. 1, Chapter 1. (c) Huheey, J. E. Inorganic Chemistry: Principles of Struerure und Reactiuity; 3rd ed.;Harper and Row: New York, 1983; pp 144-160,845-848. (d) Moeller, T.C. Inogrrnic Chemistv: A Mcdern Introductiion;Wiley: New York, 1982; pp 80-86. (e) Batsanov, S. S. Russ. Chem. Rev. (Engl. Trunsl.) 1982. 51,684-697; Usp. Khim. 1982, SI, 1201-1224. (0Pauling. L. The Nuture ofthc Chemical Bond, 3rd ed.;Comell University prtss: Itbaca, New York, 1960, Chapter 3. (g) Pauling, L. General Chemistry; W. H. Freeman and Company: San Francisco, 1970; pp 182-189. (h) Gordy, W.; Thomas, W. J. 0.1.Chem. Phys. 19!46,24,439-444. (i) Pritchard, H. 0.; Skinner, H. A. C h . Rev.1955.55,745-786. (j) Pauling, L.J. Am. Chem. Soc. 1932, 54, 3570-3582.
This appeal reflects the continuing efforts of chemists to view matter from a discrete, atomic perspective.* To be able to understand properties and reactivities of not only isolated molecules but liquids and solids as well in terms of a single number characteristic of each element is unquestionably useful and attractive. The use of electronegativities to understand bond energy differences is widely appreciated.'J However, there are many other important uses as well. For example, a striking dependence of the superconducting transition temperature on electronegativity is found for both solid elements4 and the new high-temperature superconductors.s Further, the theoretical underpinning recently (2) Strong, L. E. J . Chem. Educ. 1971,48, 562-565. (3) (a) Reddy, R. R.; Rao, T. V. R.; Viswanath, R. J . Am. Chem. Soe. 1989, l I I , 2914-2915. (h) Matcha, R. L. J. Am. Chem.Soc. 1983, 105, 4859-4862. (c) Bratsch, S.G. Polyhedron 1988,7,1677-1685. (d) Myers, R. T. J. Chem. Educ. 1979,56,711-712. (e) For the special case of metal cation solvation, .see: Qureshi, P. M.; Varshncy, R. K.;Singh, S. B. J. Chem. Educ. 1989.66.903-906. (4) (a) Luo,Q. G.; Wang, R. Y. J. Phys. Chem.Solids 1987.48,425-430. (h) Ichikawa, S.J. Phys. Chem. Solids 1989,50,931. (c) Balasuhramanian, S.;Rao. K. J. Solid Srute Commun. 1989, 71, 979-982.
0002-1863/90/ 15 12-4741%02.50/0 0 1990 American Chemical Society
